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For every pair of positive integers p > q we construct a one-relator group Rp,q whose Dehn function is ≃ n2α where α = log2(2p/q). The group Rp,q has no subgroup isomorphic to a Baumslag-Solitar group BS(m, n) with m != ±n, but it is not automatic, not CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a long-standing question on the automaticity of one-relator groups and gives counterexamples to a conjecture of Wise. [ABSTRACT FROM AUTHOR]

We prove that the second homology group of the completion of an infinite dimensional free Lie algebra is uncountable. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $ \mathfrak{g}\otimes \mathbb{C}[t,t^{-1},u\vert u^2=(t^2-b^2)(t^2-c^2)]$ [ABSTRACT FROM AUTHOR]

We construct new irreducible weight modules over quantum affine algebras of type I with all weight spaces infinite dimensional. These modules are obtained by parabolic induction from irreducible modules over the Heisenberg subalgebra. [ABSTRACT FROM AUTHOR]

We study codimension growth of infinite dimensional Lie superalgebras over an algebraically closed field of characteristic zero. We prove that if a Lie superalgebra L is a Grassmann envelope of a finite dimensional simple Lie algebra, then the PI-exponent of L exists and is a positive integer. [ABSTRACT FROM AUTHOR]